A213839 - OEIS

%I #18 Jun 17 2017 02:59:44

%S 1,20,89,240,505,916,1505,2304,3345,4660,6281,8240,10569,13300,16465,

%T 20096,24225,28884,34105,39920,46361,53460,61249,69760,79025,89076,

%U 99945,111664,124265,137780,152241,167680

%N Principal diagonal of the convolution array A213838.

%H Clark Kimberling, <a href="/A213839/b213839.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = (8*n - 21*n^2 + 16*n^3)/3.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

%F G.f.: f(x)/g(x), where f(x) = x*(1 + 16*x + 15*x^2) and g(x) = (1-x)^4.

%t (See A213838.)

%t LinearRecurrence[{4,-6,4,-1},{1,20,89,240},40] (* _Harvey P. Dale_, Mar 10 2013 *)

%Y Cf. A213838.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jul 05 2012